AMC 8 · 2012 · #3

Grade 4 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation

unit-conversionmulti-digit-arithmeticplace-value identify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Medium solution 💡 2 insights

Problem

On February 13, the newspaper reports daylight as 10 hours 24 minutes, sunrise at 6{:}57 AM, and sunset at 8{:}15 PM. The daylight length and sunrise are correct, but the printed sunset is wrong. Find the actual sunset time.

Pick an answer.

(A)

5:10 PM

(B)

5:21 PM

(C)

5:41 PM

(D)

5:57 PM

(E)

6:03 PM

AMC 8 2012 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

Sunset = sunrise + daylight is a single sum, but it is cleaner to split it into two subproblems (Tool #7): add the hours, then add the minutes, then carry. After computing, Tool #3 (Eliminate Possibilities) lets us check the answer against the five choices — a free verification on any AMC multiple-choice problem. Tool #8 (Units) is implicitly used, but the bookkeeping here is hours vs. minutes, not a unit conversion across systems, so #7 captures the structure best.

1STEP 1

Daylight runs from sunrise to sunset, so the correct sunset equals sunrise plus the daylight length; ignore the misprinted one.

sunset = 6{:}57 AM + 10 h 24 min

2STEP 2

Add the hours: 6 (from 6{:}57) plus 10 hours of daylight gives 16 hours.

6 + 10 = 16 h

3STEP 3

Add the minutes: 57 plus 24 gives 81 minutes.

57 + 24 = 81 min

4STEP 4

81 minutes tops 60, so trade 60 for 1 hour: 21 minutes are left and the hours climb to 17, giving 17 h 21 min.

81 min = 60 min + 21 min = 1 h 21 min, so total = 17 h 21 min

5STEP 5

Subtract 12 from the hours: 17{:}21 becomes 5{:}21 PM, which is choice (B).

17 - 12 = 5 → 17{:}21 = 5{:}21 PM → (B)

Answer

5:21 PM

Quick sanity check: 10 hours 24 minutes after 6{:}57 AM should land in the late afternoon. Round to 11 hours after 7 AM, that is roughly 6 PM, so a sunset near 5 to 6 PM is plausible. The exact value 5{:}21 PM sits in that window. Reverse-check: from 5{:}21 PM back to 6{:}57 AM, count from 6{:}57 AM to 5{:}21 PM as 5 hours 3 minutes to noon, plus 5 hours 21 minutes after noon, totaling 10 hours 24 minutes. Matches.

💡Key takeaway

If you can add hours, add minutes, and carry 60 minutes as 1 hour, you have all the Grade 4 skills this AMC 8 problem needs.

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